I'm a hairdresser, I lived in the USA 11 years and would normally tip my hairdresser over there 15-20% because she was good and self employed (renting a chair in a salon). Over here, I have a couple of friends who are hairdressers cut/color my hair for free (and vice versa).
Hairdressers in the USA are the same as in the UK............some are employed on a minimum wage basis and some are renting a chair. In fact most in the USA are self-employed now, renting chairs, finding salaried positions is getting harder in the USA.
In the UK salaried positions for already qualified hairdressers are getting less and less, it is more common now for hairdressers to be self-employed. I just got offered a job recently renting a chair at £150.00 per week (+ now the government is adding 20% VAT to the chair rental price which is ridiculous). That is quite a cost to put up front before even taking in clients. I would have to have back to back clients to make any kind of salary. They always advertise "Earnings equivalent to NMW (National Minimum Wage)", you can always earn more with more clients but it will take years to build up a big client list. You can see why I can't do it. I either need a salaried job and build up my clients that way and then take those clients to a new job renting a chair or build up clients as a mobile hairdresser which is what I am doing now. As a mobile hairdresser I charge less than a shop as you (the client) won't have the same experience as in a salon obviously but I have to buy all my own products and pay for gas etc.. getting to a clients house.
It is up to you if you want to tip..........I would not tip a salaried hairdresser but I would tip a self-employed hairdresser. They are no different to the self-employed hairdressers in the USA. During your conversation you can ask whether they have to rent their chair or not to find out whether you should tip. I would also tip the mobile hairdresser as they also have a lot of up-front costs that a salaried hairdresser doesn't, also the self-employed hairdresser has access to all the products in the salon.
Us mobile hairdressers are worth checking out, we are (most of us) qualified (not all salon hairdressers are believe it or not, you actually don't have to be qualified or licensed in the UK to cut hair). I would also ask your mobile hairdresser (or salon HD) if they are qualified (either NVQ Level 2 or NVQ Level 3 of which I am) and if they have liability insurance, any good HD will have at least one of those but hopefully 2 or better yet all 3 :-). I have had my hair cut in the UK by an unqualified (salon apprentice) hairdresser who was essentially being trained by the salon, I was not impressed, no H&S training and only trained to the standard of the salon owner who may have out dated skills. I have also NEVER had a skin test or a consultation (finding out about lifestyle, allergies, desired service etc..) when I have been in a salon (here in the UK & in the USA) for hair color/cut, I find that really shocking. I will always routinely do a skin test and consultation. You can actually die from having your hair colored believe it or not, I would never risk that. Mobile hairdressers rely on word of mouth only so it is important to keep our clients happy & safe, we are more likely to go on courses (out of our own pocket) to keep our skills up to date. These are just a few things to ponder.